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Likelihood for chi_eff vs. q correlations

The likelihood used for the chi_eff vs. q correlation measurements is defined in spin_v_q_likelihood.py

This analysis takes as input several dictionaries containing preprocessed or precomputed data.

  1. A dictionary containing found injections passing our FAR/SNR threshold, created by prep_injections.py; see #2 (closed). This dictionary contains the following info:

    • injectionDict['m1']: Source-frame primary masses of found injections
    • injectionDict['m2']: Source-frame secondary masses of found injections
    • injectionDict['s1z']: Primary spin z-components for found injections
    • injectionDict['s2z']: Secondary spin z-components for found injections
    • injectionDict['weights']: Precomputed factors of (p_\mathrm{inj}(m_1,m_2,\chi_\mathrm{eff},z))^{-1} for each found injection, used to enable estimate of the detection efficiency for any proposed set of hyperparameters.

  2. A dictionary of posterior samples for each event is created by the notebook preprocess_samples_conditionalEval.ipynb, under review in Issue #1 (closed). This dictionary stores samples and reweighting info in the following form:

    • sampleDict[event]['m1']: Array of source-frame primary mass samples
    • sampleDict[event]['m2']: Array of source-frame secondary mass samples
    • sampleDict[event]['Xeff']: Array of chi_effective samples
    • sampleDict[event]['z']: Array of redshift samples
    • sampleDict['Xeff_priors']: Marginal prior on chi_effective, given a prior that is uniform in component spin magnitude and isotropic in component spin orientation
    • sampleDict[event]['weights']: Pre-computed factors to reweight masses and redshifts from the default PE prior p(m_1,m_2,z) \propto (1+z)^2 D_L(z)^2 to a prior p(m_1,m_2,z) \propto \frac{1}{1+z} \frac{dV_c}{dz} (1+z)^2.

The models adopted for each parameters are the following:

  • A power law + peak model for p(m_1)
    • with power law index lmbda
    • upper power law cutoff mMax
    • peak location m0
    • peak width sigM
    • peak mixture fraction fPeak
    • lower power law cutoff is fixed to mMin=5.
  • A power law for p(m_2|m_1)
    • power law index bq
  • Redshift distribution growing as p(z)\propto \frac{dV_c}{dz} (1+z)^{\kappa-1}
    • evolution parameter kappa
  • A Gaussian for p(\chi_\mathrm{eff}) with mass-ratio dependent mean \mu_\chi(q) = \mu_{\chi,0} + \alpha(q-0.5) and standard deviation \log_{10}\sigma_\chi(q) = \log_{10}\sigma_{\chi,0} + \beta(q-0.5)
    • Mean "intercept" mu0
    • Std deviation "intercept" sigma0
    • Slope of mean with q alpha
    • Slope of log-std deviation with q beta

I implement the population likelihood that has been marginalized over total rate:

p(\{d\}|\Lambda) \propto \xi(\Lambda)^{-N} \prod_{\mathrm{Events}\,i=1}^N \Big\langle \frac{p(\theta_{ij}|\Lambda)}{p_\mathrm{prior}(\theta_{ij})}\Big\rangle_{\mathrm{Posterior\,samples}\,j},

The detection efficiency term is added to the log-likelihood in Line 127, while the sample averaging for each event is calculated and contributed to the log-likelihood in Lines 164 and 167.

Edited by Thomas Callister